Three-body unitarity with isobars revisited

Mai, M.; Hu, B.; Döring, M.; Pilloni, A.; Szczepaniak, A.

doi:10.1140/epja/i2017-12368-4

Title: Three-body unitarity with isobars revisited

Abstract

The particle exchange model of hadron interactions can be used to describe three-body scattering under the isobar assumption. Here, we start from the 3->3 scattering amplitude for spinless particles, which contains an isobar-spectator scattering amplitude. Using a Bethe-Salpeter Ansatz for the latter, we derive a relativistic three-dimensional scattering equation that manifestly fulfills three-body unitarity and two-body unitarity for the sub-amplitudes. Furthermore, this property holds for energies above breakup and also in the presence of resonances in the sub-amplitudes.

Authors:

Mai, M. ^[1]; Hu, B. ^[1]; Döring, M. ^[2]; Pilloni, A. ^[3]; Szczepaniak, A. ^[4]

George Washington Univ., Washington, DC (United States)
George Washington Univ., Washington, DC (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Indiana Univ., Bloomington, IN (United States). Center for Exploration of Energy and Matter, Physics Dept.

Publication Date:: 2017-09-08

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); National Science Foundation (NSF)

OSTI Identifier:: 1389749

Report Number(s):: JLAB-THY-17-2496; DOE/OR/23177-4206; arXiv:1706.06118
Journal ID: ISSN 1434-6001; PII: 920

Grant/Contract Number:: AC05-06OR23177; SC001658; PHY-1452055; 1415459

Resource Type:: Accepted Manuscript

Journal Name:: European Physical Journal. A

Additional Journal Information:: Journal Volume: 53; Journal Issue: 9; Journal ID: ISSN 1434-6001

Publisher:: Springer

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Mai, M., Hu, B., Döring, M., Pilloni, A., and Szczepaniak, A. Three-body unitarity with isobars revisited.  United States: N. p., 2017. 
Web.  doi:10.1140/epja/i2017-12368-4.

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                    Mai, M., Hu, B., Döring, M., Pilloni, A., & Szczepaniak, A. Three-body unitarity with isobars revisited.  United States.  https://doi.org/10.1140/epja/i2017-12368-4

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                    Mai, M., Hu, B., Döring, M., Pilloni, A., and Szczepaniak, A. Fri .  
"Three-body unitarity with isobars revisited".  United States.  https://doi.org/10.1140/epja/i2017-12368-4.  https://www.osti.gov/servlets/purl/1389749.

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@article{osti_1389749,

  title        = {Three-body unitarity with isobars revisited},

  author       = {Mai, M. and Hu, B. and Döring, M. and Pilloni, A. and Szczepaniak, A.},

  abstractNote = {The particle exchange model of hadron interactions can be used to describe three-body scattering under the isobar assumption. Here, we start from the 3->3 scattering amplitude for spinless particles, which contains an isobar-spectator scattering amplitude. Using a Bethe-Salpeter Ansatz for the latter, we derive a relativistic three-dimensional scattering equation that manifestly fulfills three-body unitarity and two-body unitarity for the sub-amplitudes. Furthermore, this property holds for energies above breakup and also in the presence of resonances in the sub-amplitudes.},

  doi          = {10.1140/epja/i2017-12368-4},

  journal      = {European Physical Journal. A},

  number       = 9,

  volume       = 53,

  place        = {United States},

  year         = {2017},

  month        = {9}

}

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text, January 2018

Döring, M.; Hammer, H. -W.; Mai, M.
GSI Helmholtzzentrum fuer Schwerionenforschung, GSI, Darmstadt
DOI: 10.15120/gsi-2019-00687

Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
text, January 2017

Hammer, H. -W.; Pang, J. -Y.; Rusetsky, A.
arXiv
DOI: 10.48550/arxiv.1707.02176

Three-body Unitarity in the Finite Volume
text, January 2017

Mai, M.; Döring, M.
arXiv
DOI: 10.48550/arxiv.1709.08222

Nucleon form factors in dispersively improved Chiral Effective Field Theory II: Electromagnetic form factors
text, January 2017

Alarcón, J. M.; Weiss, C.
arXiv
DOI: 10.48550/arxiv.1710.06430

Three-body spectrum in a finite volume: the role of cubic symmetry
text, January 2018

Döring, M.; Hammer, H. -W.; Mai, M.
arXiv
DOI: 10.48550/arxiv.1802.03362

Numerical study of the relativistic three-body quantization condition in the isotropic approximation
text, January 2018

Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
arXiv
DOI: 10.48550/arxiv.1803.04169

Variational approach to $N$-body interactions in finite volume
text, January 2018

Guo, Peng; Döring, Michael; Szczepaniak, Adam P.
arXiv
DOI: 10.48550/arxiv.1810.01261

Three-particle systems with resonant subprocesses in a finite volume
text, January 2018

Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
arXiv
DOI: 10.48550/arxiv.1810.01429

Three-body scattering: Ladders and Resonances
text, January 2019

Mikhasenko, M.; Wunderlich, Y.; Jackura, A.
arXiv
DOI: 10.48550/arxiv.1904.11894

Three-body unitarity versus finite-volume $π^+π^+π^+$ spectrum from lattice QCD
text, January 2019

Mai, M.; Döring, M.; Culver, C.
arXiv
DOI: 10.48550/arxiv.1909.05749

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Three-body spectrum in a finite volume: The role of cubic symmetry

Journal Article Döring, M. ; Hammer, H. -W. ; Mai, M. ; ... - Physical Review D

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allowmore »« less
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Title: Three-body unitarity with isobars revisited

Abstract

Citation Formats

Hadron Spectroscopy with CLAS and CLAS12 journal, January 2015

Three-body final state interaction in η→ 3π updated journal, August 2017

Spectrum of Three-Body Bound States in a Finite Volume journal, March 2015

Relativistic Three-Body Theory with Applications to π − N Scattering journal, October 1968

Coupled-channel analysis of D + → K − π + π + decay journal, January 2016

A three-body calculation of πd scattering journal, March 1976

Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles journal, April 2017

Analysis of Three-Hadron Final States journal, October 1973

Binding energy of the X ( 3872 ) at unphysical pion masses journal, December 2015

Dispersion-theoretical analysis of the D + → K − π + π + Dalitz plot journal, October 2015

Unitarity effects in pion-production isobar amplitudes journal, October 1975

The COMPASS experiment at CERN journal, July 2007

E (1420) meson as a KK¯ π molecule journal, August 1990

Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model journal, October 2009

Relativistic, model-independent, three-particle quantization condition journal, December 2014

Three particles in a finite volume journal, May 2012

Nucleon resonances within a dynamical coupled-channels model of π N and γ N reactions journal, September 2013

ω → π 0 γ * and ϕ → π 0 γ * transition form factors in dispersion theory journal, September 2012

Heavy-quark QCD exotica journal, March 2017

Recoil corrections in antikaon-deuteron scattering journal, March 2015

Unitary coupled-channels model for three-mesons decays of heavy mesons journal, December 2011

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude journal, December 2015

Minimal three-body equations with finite-range effects journal, October 1975

Towards three-body unitarity in D + → K − π + π + journal, November 2011

Minimal Three-Body Scattering Theory journal, July 1974

Coupled-channel dynamics in the reactions πN → πN, ηN, KΛ, KΣ journal, April 2013

The optical potential on the lattice journal, June 2016

Dispersive analysis of ω→3π and ϕ→3π decays journal, May 2012

Three-body resonances in two-meson–one-baryon systems journal, April 2008

Nature of the a 1 ( 1420 ) journal, May 2015

Three-body D D ¯ π dynamics for the X ( 3872 ) journal, October 2011

Relevance of complex branch points for partial wave analysis journal, July 2011

Unitary analytic isobar model for the reaction nucleon-meson to nucleon-meson-meson journal, June 1978

Theoretical support for the π ( 1300 ) and the recently claimed f 0 ( 1790 ) as molecular resonances journal, October 2011

Dispersion relations for $$\eta '\rightarrow \eta \pi \pi $$ η ′ → η π π journal, July 2017

Pion-Pion Scattering and K ± → 3 π Decay journal, August 1960

Scattering of unstable particles in a finite volume: The case of π ρ scattering and the a 1 ( 1260 ) resonance journal, March 2012

Three - Meson Resonances in a Relativistic Faddeev - Type Approach journal, September 1972

Dynamical coupled-channels model of K − p reactions: Determination of partial-wave amplitudes journal, December 2014

Eta photoproduction in a combined analysis of pion- and photon-induced reactions journal, June 2015

Faddeev-chiral unitary approach to the K − d scattering length journal, March 2013

Dispersive approaches for three-particle final state interaction journal, October 2015

Isobar formalism and one-pion-exchange partial-wave cross sections in π N → π π N journal, July 1977

Dispersive analysis of ω / ϕ → 3 π , π γ * journal, May 2015

Remarks on study of X ( 3872 ) from effective field theory with pion-exchange interaction journal, February 2015

New approach to the theory of coupled πNN-NN systems journal, April 1980

Relativistic isobar model: Spinless particles journal, May 1976

Hadron Spectroscopy at BESIII journal, April 2016

Reduction of the three-particle collision problem to multi-channel two-particle Lippmann-Schwinger equations journal, June 1967

The Physics of the B Factories journal, November 2014

Multiquark resonances journal, January 2017

Three-body final state interaction in η → 3 π journal, September 2015

Linear Integral Equations for Relativistic Multichannel Scattering journal, February 1966

Unified theory of γN→πN , ππN , and πN→πN , ππN reactions journal, October 1988

Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data journal, October 2017

New approach to the theory of coupled πNN-NN systems journal, February 1981

The Compass Experiment at CERN conference, January 2005

Three particles in a finite volume conference, October 2012

Recoil corrections in antikaon-deuteron scattering conference, June 2016

The Physics of the B Factories text, January 2014

The COMPASS experiment at CERN conference, January 1997

Hadron Spectroscopy at BESIII journal, December 2018

The Physics of the B Factories text, January 2014

New approach to the theory of coupled πNN-NN systems journal, September 1979

Recoil corrections in antikaon-deuteron scattering journal, January 2016

Hadron Spectroscopy at BESIII journal, January 2016

Unitary coupled-channels model for three-mesons decays of heavy mesons text, January 2011

Faddeev-Chiral Unitary Approach to the $K^- d$ scattering length text, January 2012

Dynamical coupled-channels model of $K^- p$ reactions (I): Determination of partial-wave amplitudes text, January 2014

A relativistic, model-independent, three-particle quantization condition text, January 2014

Recoil corrections in antikaon-deuteron scattering text, January 2014

Eta photoproduction in a combined analysis of pion- and photon-induced reactions text, January 2015

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude text, January 2015

Heavy-Quark QCD Exotica text, January 2016

Multiquark Resonances text, January 2016

Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles text, January 2017

Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data text, January 2017

Hadron Spectroscopy with CLAS and CLAS12
journal, January 2015

Three-body final state interaction in η→ 3π updated
journal, August 2017

Spectrum of Three-Body Bound States in a Finite Volume
journal, March 2015

Relativistic Three-Body Theory with Applications to $π - N$ Scattering
journal, October 1968

Coupled-channel analysis of $D^{+} \to K^{-} π^{+} π^{+}$ decay
journal, January 2016

A three-body calculation of πd scattering
journal, March 1976

Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
journal, April 2017

Analysis of Three-Hadron Final States
journal, October 1973

Binding energy of the $X (3872)$ at unphysical pion masses
journal, December 2015

Dispersion-theoretical analysis of the D + → K − π + π + Dalitz plot
journal, October 2015

Unitarity effects in pion-production isobar amplitudes
journal, October 1975

The COMPASS experiment at CERN
journal, July 2007

E (1420) meson as a KK¯ π molecule
journal, August 1990

Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model
journal, October 2009

Relativistic, model-independent, three-particle quantization condition
journal, December 2014

Three particles in a finite volume
journal, May 2012

Nucleon resonances within a dynamical coupled-channels model of $π N$ and $γ N$ reactions
journal, September 2013

$ω \to π^{0} γ^{}$ and $ϕ \to π^{0} γ^{}$ transition form factors in dispersion theory
journal, September 2012

Heavy-quark QCD exotica
journal, March 2017

Recoil corrections in antikaon-deuteron scattering
journal, March 2015

Unitary coupled-channels model for three-mesons decays of heavy mesons
journal, December 2011

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
journal, December 2015

Minimal three-body equations with finite-range effects
journal, October 1975

Towards three-body unitarity in $D^{+} \to K^{-} π^{+} π^{+}$
journal, November 2011

Minimal Three-Body Scattering Theory
journal, July 1974

Coupled-channel dynamics in the reactions πN → πN, ηN, KΛ, KΣ
journal, April 2013

The optical potential on the lattice
journal, June 2016

Dispersive analysis of ω→3π and ϕ→3π decays
journal, May 2012

Three-body resonances in two-meson–one-baryon systems
journal, April 2008

Nature of the $a_{1} (1420)$
journal, May 2015

Three-body $D \bar{D} π$ dynamics for the $X (3872)$
journal, October 2011

Relevance of complex branch points for partial wave analysis
journal, July 2011

Unitary analytic isobar model for the reaction nucleon-meson to nucleon-meson-meson
journal, June 1978

Theoretical support for the $π (1300)$ and the recently claimed $f_{0} (1790)$ as molecular resonances
journal, October 2011

Dispersion relations for $$\eta '\rightarrow \eta \pi \pi $$ η ′ → η π π
journal, July 2017

Pion-Pion Scattering and $K^{\pm} \to 3 π$ Decay
journal, August 1960

Scattering of unstable particles in a finite volume: The case of $π ρ$ scattering and the $a_{1} (1260)$ resonance
journal, March 2012

Three - Meson Resonances in a Relativistic Faddeev - Type Approach
journal, September 1972

Dynamical coupled-channels model of $K^{-} p$ reactions: Determination of partial-wave amplitudes
journal, December 2014

Eta photoproduction in a combined analysis of pion- and photon-induced reactions
journal, June 2015

Faddeev-chiral unitary approach to the $K^{-} d$ scattering length
journal, March 2013

Dispersive approaches for three-particle final state interaction
journal, October 2015

Isobar formalism and one-pion-exchange partial-wave cross sections in $π N \to π π N$
journal, July 1977

Dispersive analysis of $ω / ϕ \to 3 π, π γ^{*}$
journal, May 2015

Remarks on study of $X (3872)$ from effective field theory with pion-exchange interaction
journal, February 2015

New approach to the theory of coupled πNN-NN systems
journal, April 1980

Relativistic isobar model: Spinless particles
journal, May 1976

Hadron Spectroscopy at BESIII
journal, April 2016

Reduction of the three-particle collision problem to multi-channel two-particle Lippmann-Schwinger equations
journal, June 1967

The Physics of the B Factories
journal, November 2014

Multiquark resonances
journal, January 2017

Three-body final state interaction in $η \to 3 π$
journal, September 2015

Linear Integral Equations for Relativistic Multichannel Scattering
journal, February 1966

Unified theory of γN→πN , ππN , and πN→πN , ππN reactions
journal, October 1988

Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data
journal, October 2017

New approach to the theory of coupled πNN-NN systems
journal, February 1981

The Compass Experiment at CERN
conference, January 2005

Three particles in a finite volume
conference, October 2012

Recoil corrections in antikaon-deuteron scattering
conference, June 2016

The Physics of the B Factories
text, January 2014

The COMPASS experiment at CERN
conference, January 1997

Hadron Spectroscopy at BESIII
journal, December 2018

The Physics of the B Factories
text, January 2014

New approach to the theory of coupled πNN-NN systems
journal, September 1979

Recoil corrections in antikaon-deuteron scattering
journal, January 2016

Hadron Spectroscopy at BESIII
journal, January 2016

Unitary coupled-channels model for three-mesons decays of heavy mesons
text, January 2011

Faddeev-Chiral Unitary Approach to the $K^- d$ scattering length
text, January 2012

Dynamical coupled-channels model of $K^- p$ reactions (I): Determination of partial-wave amplitudes
text, January 2014

A relativistic, model-independent, three-particle quantization condition
text, January 2014

Recoil corrections in antikaon-deuteron scattering
text, January 2014

Eta photoproduction in a combined analysis of pion- and photon-induced reactions
text, January 2015

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
text, January 2015

Heavy-Quark QCD Exotica
text, January 2016

Multiquark Resonances
text, January 2016

Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
text, January 2017

Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
text, January 2017

The COMPASS Experiment at CERN
text, January 2007

Three-body scattering: ladders and resonances
journal, August 2019

Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data
journal, October 2017